Topologies and structures of the Cremona groups

Original · EN

We study the algebraic structure of the n-dimensional Cremona group and show that it is not an algebraic group of infinite dimension (ind-group) if n≥ 2. We describe the obstruction to this, which is of a topological nature. By contrast, we show the existence of a Euclidean topology on the Cremona group which extends that of its classical subgroups and makes it a topological group.